Background: The ramifications of COVID-19 restrictions might accelerate the already rising proportion of children with overweight or obesity. Objectives: To assess the association between COVID-19 restrictions and changes in body mass index (BMI) and the proportion of children with overweight or obesity. Methods: Cohort study with baseline measurements in September 2019 (prior to COVID-19 restrictions) and follow-up in June 2020, September 2020, and March 2021 at 12 primary schools in Austria. The height and weight of 738 children aged 7 to 10 years were measured and age- and sex-specific national and international standardized values were calculated. Changes over time were analysed by analysis of variance. Results: Mean BMI IOTF standard deviation scores (SDS) increased by 0.24 (95% CI, 0.21–0.28) between September 2019 and March 2021. The proportion of children with overweight or obesity increased from 20.7% to 26.2% during this period (p < 0.001) using national reference values—EQUI BMI AUT—comparable results were observed. Simultaneously, the height AUT SDS increased by 0.06 (95% CI, 0.05–0.08) with a larger increase in girls (+0.11; p < 0.001) than in boys (+0.03; p = 0.19). Conclusions: COVID-19 restrictions were associated with accelerated increases in mean BMI and the proportion of children with overweight or obesity. The increase in height SDS in girls calls for further investigations.